Cube in a sphere

The cube is inscribed in a sphere with volume 7253 cm3. Determine the length of the edges of a cube.

Result

a =  13.9 cm

Solution:

V=7253 cm3 V=43πr3  r=3 V4π3=3 72534 3.1416312.0082 cm  D=2 r=2 12.008224.0163 cm  u=D=24.016324.0163 cm  u=3a  a=u/3=24.0163/313.865813.9 cmV=7253 \ \text{cm}^3 \ \\ V=\dfrac{ 4 }{ 3 } \pi r^3 \ \\ \ \\ r=\sqrt[3]{ \dfrac{ 3 \cdot \ V }{ 4 \pi } }=\sqrt[3]{ \dfrac{ 3 \cdot \ 7253 }{ 4 \cdot \ 3.1416 } } \doteq 12.0082 \ \text{cm} \ \\ \ \\ D=2 \cdot \ r=2 \cdot \ 12.0082 \doteq 24.0163 \ \text{cm} \ \\ \ \\ u=D=24.0163 \doteq 24.0163 \ \text{cm} \ \\ \ \\ u=\sqrt{ 3 } a \ \\ \ \\ a=u/\sqrt{ 3 }=24.0163/\sqrt{ 3 } \doteq 13.8658 \doteq 13.9 \ \text{cm}



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Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 2 comments:
#
Math student
i am good at this

2 years ago  2 Likes
#
Crazy Butterfly
This is easy.

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